I have the same problem. I live in Turkey and have a Mac mini M2. When I first downloaded the launcher and tried to download UE5.7, it downloaded fine. But then I wanted to download UE4.27 because UE5.7 was lagging. I deleted it and tried downloading 4.27, but I got an MD-DL-200 error after about 2 minutes of initialization. This has been going on for three days now. (I also tried changing the router settings and using VPN)
Been a long time and several versions of Unreal but I found a fix to let the Launcher download the app. I do not know how legit it is but I am currently downloading 5.8 as I type.
So if you have the same problem I had then try these steps:
On the MAC only:
1/ Close Epic Launcher
2/ Go to Applications folder and select the app
3/ Right Click on it or Control click on it
4/ Select show package contents from the drop-down menu
ALL THESE STEPS HAPPEN WITHIN THE PACKAGE ITSELF:
5/ Open the contents folder
6/ Open UE folder
7/ Open EpicGamesLauncher folder
8/ Open Config folder
9/ Open DefaultEngine.ini file
10/ About 12 lines down is the [HTTP] section
11/ Delete the first line of that section it says: HttpTotalTimeout=##
(This was killing the network precesses and stopping the download.
You can always note what the line says and replace it later.)
12/ Save the changes
13/ Close all folders and reopen the Launcher and cross your fingers.
As I said it is working for me. You can alway replace the line after you are done.